Răspuns:
a)3375/2
b)9cm
Explicație pas cu pas:
Duci DM_|_AB
Atunci vom avea DM=BC=45cm
Dar stim ca mA=45 => triunghiul AMD dreptunghic isoscel => DM=AM=45cm =>AB=45+15=60cm (AM+CD)
A ABCD=(AB+CD)×BC/2=75×45/2
Ducem diagonala AC si aplicam in triunghiul ACB T.P => AC²=AB²+BC² =>
AC²=60²+45² => AC=75cm
A ACB=AB×BC/2=60×45/2
=>A ACD=A ABCD-A ACB =>
A ACD=75×45/2 - 45×60/2 =>
A ACD=45(75-60)/2 =>
A ACD=45×15/2=675/2
Notam DN_|_AC => DN×AC/2=675/2 =>
DN×AC=675 => DN×75=675 =>DN=9
